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Tagged: equations, Simultaneous Equations, Standard
Solve simultaneously: 2x + y = 8, y = 4x – 10.
substitute y = 4x – 10 into second equation 2x + (4x – 10) = 8 6x – 10 = 8 6x = 18 x = 3
y = 4(3) – 10 y = 12 – 10 y = 2 ∴ x = 3, y = 2
Solve: 3x – 5y = 28 and x + 4y = 15
multiply the second one by 3 to make the x’s the same
3x + 12y = 45 – 3x – 5y = 28
3x – 3x + 12y – -5y = 45 – 28
17y = 17
y = 1
x + 4(1) = 15
x + 4 = 15
x = 11
∴ x = 11, y = 1
Solve simultaneously: 2x – 4y = 2, x = -2y + 9.
substitute the second equation into the ‘x’ of the first one
2(-2y + 9) -4y = 2 -4y + 18 – 4y = 2 -8y = -16 y = 2
x = -2(2) + 9 x = -4 + 9 x = 5
x = 1, y = 5
Solve simultaneously: 7a + 3b = 4, 5a + 2b = 3.
7a + 3b = 4 ×2 5a + 2b = 3 ×3
14a + 6b = 8 – 15a + 6b = 9 -a = -1 a = 1
7(1) + 3b = 4 7 + 3b = 4 3b = -3 b = -1 ∴ a = 1, b = -1